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2 Answers
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Sneak attack's damage type is the same as the weapon used to deliver the attack

Sneak Attack says:

Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a ranged weapon.

All the ability does it take the original source of damage and add more damage to it. It is still considered one attack and one source of damage. And the thing that determines the damage type of an attack/source of damage is whatever caused that attack. In most cases of sneak attack, that is the weapon used to deliver the attack.

Sneak Attack relies entirely on the weapon you're using. The weapon sets the damage type of the extra damage, and the weapon determines whether you can Sneak Attack at all; the weapon must be in the ranged category or have the finesse property.

So it should be abundantly clear by RAW and RAI that sneak attack is the same damage type as the weapon you use.

There is no such thing as magic damage, but sneak attack can be part of a magical attack

"Magic" is not a damage type. In fact, the only thing that matters is if the attack itself is considered magical and only then for the purposes of bypassing resistance to attacks that aren't magical.

Some creatures have vulnerability, resistance, or immunity to certain types of damage. Particular creatures are even resistant or immune to damage from nonmagical attacks (a magical attack is an attack delivered by a spell, a magic item, or another magical source). (Basic Rules, p. 112)

So, if you are dealing sneak attack damage as part of a magical attack, the damage from sneak attack is considered part of that.

There is no contradiction with Great Weapon Fighting

There is no contradiction in ruling like you might be seeing.

Great Weapon Fighting says:

When you roll a 1 or 2 on a damage die for an attack you make with
a melee weapon that you are wielding with two hands, you can reroll
the die and must use the new roll, even if the new roll is a 1 or a 2.
The weapon must have the two-handed or versatile property for you to
gain this benefit.

The Sage Advice Compendium explicitly states the intended reading of this rule however:

The Great Weapon Fighting feature—which is shared by fighters and
paladins—is meant to benefit only the damage roll of the weapon used
with the feature. For example, if you use a greatsword with the
feature, you can reroll any 1 or 2 you roll on the weapon’s 2d6. If
you’re a paladin and use Divine Smite with the greatsword, Great
Weapon Fighting doesn’t let you reroll a 1 or 2 that you roll for the
damage of Divine Smite.

Even though Sneak Attack inherits its damage type from the weapon used, that does not mean that it is damage dice of the weapon itself. Only the damage listed on that weapon and its effects count as a weapon's damage dice. Thus, Sneak Attack does not qualify for GWF rerolls under the RAI.

However, this causes no contradictions with the ruling on Sneak Attack's damage type above. In fact, this discussion has no link to the damage type of Sneak Attack at all.

Damage Types

Damage types have no rules of their own, but other rules, such as
damage resistance, rely on the types. The damage types follow, with
examples to help a DM assign a damage type to a new effect. (edited
for brevity (Basic Rules, p. 75)) Acid. Bludgeoning. Cold. Fire. Force. Lightning. Necrotic. Piercing. Poison. Psychic. Radiant. Slashing. Thunder.

Magical isn't one of the listed damage types. Shortswords do slashing damage. (Weapons table, PHB, p. 48). Sun blades do radiant damage, and they provide magical attacks since they are magical swords. (Magic Item, see above).

Sneak Attack

Once per turn, you can deal an extra 1d6 damage to one creature you hit with an attack if you have advantage on the attack roll. The attack must use a finesse or a rangedweapon.

Note from the above: Sneak Attack's extra damage dice are bound to the weapon being used to inflict them. Many weapons cannot be used for a sneak attack, such as a quarter staff, a great club, a greataxe, a pike, a glaive, et cetera.

The amount of the extra damage increases as you gain levels in this class, as shown in the Sneak Attack column of the Rogue table.

From a practical standpoint, if the sneak attack did not do the weapon's damage type, there would be a serious nerf on the Rogue class since that is a major feature of their combat capability.

Sneak Attack and the Great Weapon Fighting fighting style have no relationship to each other. (Aside: the game wasn't balanced for multiclassing; multiclassing is an optional/variant rule. More on this later). There are no weapons on the weapon table that are finesse that you can use for Great Weapon Fighting. (There is one magical weapon (rare) that is an exception to the rule: Sun Blade, which is has the finesse property. The rule on Specific Beats General (Basic Rules, p. 5) handles that lone exception well enough.

There is no contradiction; there is an exception. And here's the thing: GWF is a Fighter class feature. The tweet response was about a Fighter class feature, not a Rogue class feature. Sneak attack is a Rogue class feature. Under the basic RAW, multiclassing is an option, a variant rule, and the devs have stated on many occasions that the game balance efforts did not include multi-classing. You are thus in the land of rulings, not rules, at this point.

RAW supports the nova strike.

Great Weapon Fighting (Fighter and Paladin class feature)

When you roll a 1 or 2 on a damage die for an attack you make with a
melee weapon that you are wielding with two hands, you can reroll the
die and must use the new roll, even if the new roll is a 1 or a 2. The
weapon must have the two-handed or versatile property for you to gain
this benefit.

Sun blade fits all of this, so far.

Sneak Attack / Critical hit

... if you score a critical hit with a dagger, roll 2d4 for the
damage, rather than 1d4, and then add your relevant ability modifier.
If the attack involves other damage dice, such as from the rogue’s
Sneak Attack feature, you roll those dice twice as well.

Sneak Attack:
you can deal an extra 1d6 damage to one creature you hit with an attack ...

So what do I do as a DM?

If this exception seems to you to be a problem, then the simple answer is "no sun blades in this world" or "no Rogue Fighter MC with that combo." Problem solved. (Tell the players up front, please). If, on the other hand, you are willing to now and again wallow in a Sneak-Attack-Sun-Blade-Radiant-Damage nova from the Thief/Fighter Multi class, then make that ruling and play on. (The Angels and other Celestials who resist radiant damage won't worry in any case ...)

As a side note, your question mixes apples and oranges. Divine smite has no relationship to Sneak Attack. Also, Divine Smite does radiant damage, not "magical" damage.

Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage. The extra damage is 2d8 for a 1st‑level spell slot, plus 1d8 for each spell level higher than 1st ... (SRD p. 31-32)

Sneak Attack relies entirely on the weapon you're using. The weapon
sets the damage type of the extra damage, and the weapon determines
whether you can Sneak Attack at all; the weapon must be in the ranged
category or have the finesse property.

A magic item like the flame tongue and the frost brand deal extra
damage of a particular type when they hit. That extra damage doesn't
change the underlying damage type of the weapon. And it's the
weapon's damage type that is used by a feature like Sneak Attack